Jack and John are jogging along a circular track at the same speed in different lanes. Jack is running in the inner lane which has a radius of \( r_i = 30 \text{ m}, \) and John is in the outer lane of radius \( r_o = 45 \text{ m}. \) If Jack's angular speed is \( \omega_1 = 0.3 \text{ s}^{-1}, \) what is the angular speed of John?

A man is jogging along a circular track with perimeter \( r_1 = 160 \text{ m}, \) and it takes \( t_1 = 47 \text{ s} \) for him to jog around the track. If the same man jogs along a bigger track with perimeter \( r_2 = 320 \text{ m} \) with the same speed, how long will it take for him to jog around it?

Jack and John are jogging together along a circle track with the same angular speed in different lanes. Jack is on the inner lane which has radius \( 22 \text{ m}, \) and John is on the outer lane which has radius \( 30 \text{ m}. \) If the speed of Jack is \( 11 \text{ m/s}, \) what is the speed of John?